The Pentagon Attack on 9/11:
A Refutation of the Pentagon Flyover Hypothesis
Based on Analysis of the Flight Path

September 2011

Introduction

The legal and
political implications of 9/11 have turned scientific research in
this area into a high stakes competition for the minds of the public.
Pertinent information has been kept secret, the corporate media has
systematically kept "damaging" information (such as video images
of the World Trade Center Building 7) out of public view, 9/11
research has been marginalized, and the official investigations have
failed to answer, or in many cases even address, the most troubling
questions. One development that appears to be a tactic in the ongoing
cover-up is the high profile promotion of transparently false
theories, "straw men," the only purpose of which appears to be to
allow the 9/11 Truth Movement to be ridiculed.

With the tenth anniversary of 9/11 upon us, the battle for public
perceptions has intensified and there is a heightened campaign to
undermine the scientific basis of the truth movement. Dr Judy Wood
has published a book asserting that the World Trade Center (WTC)
towers were felled by "dustification" of the steel, which she
claims is achieved by the use of "directed free energy".
1
It is, however, obvious that the steel was severed and fell in normal
lengths, otherwise intact, as seen in conventional demolitions. The
similarly foolish idea that the WTC towers were demolished by nuclear
explosives, long ago refuted,
2
has also been recently revived, with a new claimant appearing, Jeff
Prager,
3
but this appears to be having little influence so far. No explanation
involving "directed free energy" or nuclear devices could account
for the way separate explosions appeared in the Twin Towers, layer by
layer, descending at a precise rate, as the towers came down.
4

It is important to
distinguish between devious false claims, intended to weaken the
truth movement, and false claims which result from accidental errors.
There can be errors of interpretation of evidence, calculation errors
and misleading testimonies from witnesses who fail to correctly
remember the event they observed and describe.

An example of an unfortunate calculation error is found in the work
of Pilots for 9/11 Truth (PFT). This group has a long-held position
that the topography near the Pentagon would rule out impact by
American Airlines Flight 77 (AA77). This position was based on a
calculation that the plane would necessarily experience an
unsurvivable force of 10.14g if it attempted to pull up from the dive
on approach to the Pentagon.
5
PFT based its calculation on a path that was somewhat different from
the path of the plane as shown in the files initially provided by the
National Transport Safety Board (NTSB), reportedly from the flight
data recorder (FDR). The NTSB data appeared to show that the flight
terminated at a point too high to have hit the Pentagon. Instead, to
make the possibility of impact more feasible, the PFT calculation was
based on the assumption that the plane actually came in much lower,
level with the top of the VDOT antenna tower near the Navy Annex. It
was shown by several researchers that this calculation was incorrect
due to a substantial error in determining the radius of the pull-up
arc. This error in turn produced an excessive value for the required
g-force. The error was increased by assuming, without
evidence, that the plane traveled in a straight line at a constant
descent angle from the top of the antenna to the first light pole
hit. If this artificial restriction is removed, and the plane is
allowed to follow a curved approach, the pull-up can be spread over a
wider arc, increasing the radius of curvature and reducing the wing
load. Calculation shows that paths can be found such that the force
generated would place no undue stress on the aircraft, being well
below the design limit of 2.5g.
6

The file provided by the NTSB certainly appeared to show the plane
was not only too high to strike the Pentagon but also was descending
too steeply to have produced the type of damage observed. This
behavior suggested to some researchers that the recording of data had
been terminated while the plane was still on descent. John Farmer
used radar data to check the FDR file data and concluded that indeed
several seconds of data was missing from the end of the file.
7
Recently Warren Stutt discovered that there was one more frame of
data at the end of the FDR file which had not been decoded
previously. He wrote a decoding program and managed to extract a
further 4 seconds of data. This data includes radio height above
ground, which now shows the plane descending smoothly, pulling up
safely and hitting the Pentagon close to the ground, in accordance
with the majority of eyewitness reports.
8
PFT is not willing to use this data as there is no proof that the
file is authentic and has not been tampered with.
9
Despite claiming that the file cannot be relied upon they use it to
claim that the final radio height was measured from the Pentagon roof
as the plane flew over. It has been shown that this argument is not
correct as the prior data points do not reveal a sudden jump upward
of the reflecting surface as the Pentagon is reached.
10

It is further argued
by PFT that the radar data must be in error as it does not correspond
with the pressure altimeter record, which still shows the plane too
high to hit the Pentagon. On approach to the Pentagon, however, the
plane is flying much faster than normal for an aircraft at low
altitude and so would be operating well beyond the calibration
envelope for the altimeter. It appears that, at least on this
particular plane, a substantial error is produced, increasing as the
plane accelerates and descends. In contrast the radio height would
not be affected by speed. It is therefore reasonable to accept the
height it shows, which corresponds with the height shown by the
damage to the light poles and the face of the Pentagon. This has been
fully discussed in a previous paper where it is shown that the
altimeter reading and radio height reading correspond closely with
each other at normal altitude and speed but diverge as the plane
descends and accelerates to abnormal speeds.
8

One of the reasons
why PFT may be reluctant to utilize the newly decoded last frame of
data in the FDR file is that the concept that the plane could not
have hit the Pentagon, and therefore must have flown over, is
supported by the Citizen Investigation Team (CIT). In this paper we
examine the flyover theory presented by CIT and find it to be false.

CIT claims (1) that
the plane approached the Pentagon along a path too far north to have
done the observed directional damage, (2) that all the damage was
faked and (3) that the plane flew over the Pentagon. The apparently
surprising claim that the plane flew over the Pentagon is a necessary
part of the CIT position as it explains the lack of damage in
alignment with the north path inside the Pentagon. CIT supports its
theory with the testimony of a small number of selected witnesses,
presented in selectively edited video interviews, who state that the
plane passed north of the former Citgo service station.
11
David Chandler and Jon Cole point out, among other things, that the
CIT "...witnesses are not representative of the overall
eyewitness pool".
12
Certainly their witnesses are not representative of the witness pool
as there are very many more witnesses to impact.
13
Gregg Roberts states that CIT's work contains "logical
fallacies".
14
CIT disputes the findings of Chandler and Cole at length
15
but provides no new evidence, and has intensified its personal
attacks on anyone who criticizes their claims in blogs and Facebook.
We do not assert that CIT is deliberately setting up false theories
in order to expose the 9/11 Truth Movement to ridicule, but that is
likely to be the ultimate effect of their efforts.

Unfortunately the
well presented videos and website of CIT have impressed a lot of
people, so dissension has arisen, which is destructive to the 9/11
Truth movement. Michiel de Boer has suggested that the accumulated
evidence that a large commercial aircraft hit and damaged the
Pentagon is now so substantial that we should plainly assert that
impact did occur.
16
The natural corollary to the proposition that impact occurred is that
the claimed north path, and consequent flyover of the Pentagon, is
false. The physical implausibility of the north path proposition will
be demonstrated in this paper.

Consideration of
prior events

During the morning
of 9/11 four planes were hijacked and the normal interception
response failed. Two of these planes hit the WTC towers. These
impacts were seen by many people and recorded on video. It cannot be
rationally disputed that they occurred. The impact on the South Tower
was recorded on several videos showing that the plane largely
penetrated the building. Very clear photographs of the impact areas
of both towers exist and it is clear that all but the wing tips
entered the buildings. Some debris fell to the street below and was
reported by eyewitnesses and photographed. The amount was small and
appeared commensurate with the portion of the impact area not
penetrated.

In the case of the
Pentagon the outer wall had been reinforced to an unusual degree
during renovation so it appears reasonable that the impact hole would
be smaller and that more of the plane would fail to penetrate the
building. Photographs and videos show the entire wingspan of the
plane damaged the face of the building but the entry hole was
smaller. On the ground outside the Pentagon a substantial amount of
debris was observed and recorded in photographs and videos. Again the
amount of debris outside appeared roughly commensurate with the
portion of the impact area not penetrated.

As two incidents had
occurred that morning in which planes had been observed to deeply
penetrate buildings, it should not have been surprising that a plane
could penetrate the Pentagon, and there was initially general
acceptance of the impact report. Unfortunately, however, a number of
observers saw the debris outside the Pentagon but did not see the
sizable hole in the wall, more than adequate to allow most of the
aircraft to enter. They reported that the amount of debris was not
sufficient. Thus was created the fertile field in which alternative
theories developed to explain the observed damage.

Discussion

The physical evidence
at the Pentagon is consistent with the view that a plane
with the wingspan of a Boeing 757 flew into the Pentagon
17
along a straight line at a heading of about 61°, damaging light
poles, a fence and a heavy generator; largely penetrated the outer
wall and caused a trail of further damage in the same direction
inside. A best-fit line through the positions reported in the fully
decoded FDR data file has a heading of 61.3° for the last 20 seconds
of flight, similar to the heading of the radar data, which places the
approach south of the former Citgo service station and therefore in
accordance with the official account. The bulk of the eyewitness
testimony is in agreement with the physical data and with these
records. Despite this persuasive evidence, CIT continues to assert
that the plane flew north of the Citgo (NOC) service station. This is
the crucial assertion as only if it is true must we give
consideration to CITs other assertions.

To explain the very
obvious damage, and to set aside the accounts of the many
eyewitnesses to impact, CIT presents the theory that the damage was
done by explosives and that the departing plane was hidden from
viewers by the rising plume of smoke from these explosives.
Contradicting this theory is the fact that most of the viewers were
to the side and would not have had their vision obscured. Also, many
of the viewers testified to seeing the actual impact. They didnt
just say they saw the explosion; they describe the low-level approach
of the plane and the impact. Some were very close and it is difficult
to imagine how they could have been mistaken.
18
It is highly improbable that a person whose eyes were fixed on the
plane as it approached the face of the Pentagon would fail to follow
it over the roof, if it had in fact flown over. The absence of
flyover witnesses is significant, given that so many people were
known to be watching the approach.

So far the arguments used against CIT have been mainly critiques of
its methods. These studies indicate that CIT carefully selected
witnesses who were prepared to say that they recalled seeing the
plane passing NOC, and have avoided interviewing, or discounted, the
many witnesses who recalled seeing the impact. There may be a handful
of people who thought the plane was north of the official flight
path, but there would have been hundreds of potential witnesses to
flyover, had it occurred, as the Pentagon has major roads passing by
it on all sides, and many vehicles were held up in traffic jams. That
a plane flying over the Pentagon would be readily seen has been amply
demonstrated by Jim Hoffman.
19
Some counter that the view of the Pentagon would be obstructed by
trees and guard rails, but there is a video from a moving car showing
that the roof of the Pentagon would be visible for a great distance
around the Pentagon.
20
Some counter that the Google Earth images are misleading as they do
not depict the buildings between the Pentagon and the surrounding
roads, but there were no buildings tall enough to block the view of
the roof of the Pentagon.

Closer examination
shows that, of the NOC witnesses, all who were in a position to see
the Pentagon reported that the plane actually hit the building or
that it was flying so low it could not miss.
21
CIT casts doubt on the testimony of the witnesses to impact by
asserting that the use of explosives, as the plane passed by, created
a "magic show" which fooled them. Many witnesses realized,
however, that the plane was about to hit the Pentagon before the
smoke appeared, so could not have been fooled by it.

By framing the direction of the approach as the central issue, CIT
calls upon the witnesses to recollect what would have seemed to them
to be a minor detail at the time, while ignoring, or explicitly
discounting, their experience of the impact that would have been the
clear focus of their attention and burned into their memory. While
CIT has found these few witnesses who agree with the NOC flight path,
it has been unable to find a single witness who endorses its over-fly
conclusion. One of their key witnesses (Lagasse) demonstrates clearly
with his hands that the plane did not hit the wall straight on, and
then says. "It kinda went in at an angle." "When the plane hit
it just kinda disappeared." He indicated that his memory of the
details may be open to question, but his memory of impact was not:
"There is only one thing that is irrefutable ... the fact is
American Airlines plane went from here into the building. You can
pick apart everything else ..."
22
Another (Turcios)
looked surprised when asked if he saw the plane fly over. He said
"No. The only thing I saw was ... direct line to go into the
Pentagon. It collided."
22
Their third key witness (Brooks), who was across the street from the
gas station, said that he watched the plane "... awfully low ...
just go nose dive into the Pentagon ... full throttle ... clip the
lamp pole ..." "... just the sheer impact ... it just literally
disintegrated the plane."
23
Clearly none of these witnesses is describing flyover and none of
them sounds uncertain or confused.

By framing the
question as they do, as a matter of approach direction, CIT cleverly
sidesteps the crucial issue, whether the plane was high or low, and
thus appears to be the party creating the real magic show.

The classic witness
to a low approach is Sean Boger, Air Traffic Controller in the
heliport tower at the Pentagon. The glassed area of the tower
extended round the side where impact occurred so he would have had an
unobstructed view of the approach and the impact. "... coming
right at us, and he didnt veer." "I am watching the plane go
all the way into the building." "Once the plane went into the
building it exploded, and once it exploded, I hit the floor and just
covered up my head. It was like glass shattering and ceiling tile was
falling ..." CIT says "more than likely he ducked," trying to
suggest that he couldnt have seen the plane hit, but Boger's
words plainly contradict this speculation.
24
Note the phrase "he didnt veer," indicating that the approach
was not curved, as would have been the case had the plane passed NOC.

CIT uses methods
which must be regarded as questionablefor a scientific
discussion and has published a list where people who disagree with
its views are named and ridiculed, apparently for the purpose of
intimidation.
25
What it does not do is apply necessary logical processes to the
debate. It does not consider evidence against its hypothesis but
simply insists that the NOC witnesses must be irrefutable because
they corroborate one another. CIT glosses over the highly pertinent
fact that the number of witnesses who corroborate impact is far
greater, and it ignores the absence of over-fly witnesses. On this
basis alone its hypothesis must be regarded as flimsy, at best.

Among the eyewitness
testimonies we find several key witnesses who locate the plane south
of the Sheraton hotel and the Navy Annex as it approached the
Pentagon. We find that three of them, Ed Paik, Terry Morin and Albert
Hemphill, are relied upon, but misrepresented, by CIT.

1. Deb Anlauf,26
from her room in the 14th floor of the Sheraton Hotel:
"Suddenly I saw this plane right outside my window," "You felt
like you could touch it; it was that close. It was just incredible."

2. Isobel James,27
News 4, 10:17. "I saw a big plane, commercial liner type, going
down full speed, inside, inside the side of the Pentagon.
Obviously it was going into the Pentagon purposely. We were driving
down Columbia Pike -- right over us." Q: "You actually saw the
plane impact the side of the building?" A: "Yes I did."

3. Ed Paik.28Eric Larson analyses the testimony of Paik, who saw the
plane pass by while he was inside his shop, looking
south through the window. The furthest north it could have been would
be Columbia Pike, and the furthest south would be a little south of
the VDOT antenna tower. CIT deceives the public by hiding the fact
that Paik was inside his shop when he saw the plane. CIT touts the
fact that they interviewed their witnesses on-site where they had
originally witnessed the events, but the Paik interview was conducted
outside, which colors his testimony. He seems to go along with CITs
idea that the plane went over the shop, but this would be impossible
to observe from his actual location. He is listed as a north path
witness but should not be, as he and his brother speculated that the
plane may have damaged the VDOT tower, which would indicate a south
path, as they noticed something was bent on the tower and saw work
being done there the next day.

4. Terry Morin.29
On the referenced website Morin carefully explains how he was able to
see the plane descending until it partially disappeared behind some
trees.

"... the noise was absolutely deafening." "The aircraft was
essentially right over the top of me and the outer portion of the FOB
(flight path parallel the outer edge of the FOB)." "Within
seconds the plane cleared the 8th Wing of BMDO and was heading
directly towards the Pentagon. Engines were at a steady
high-pitched whine, indicating to me that the throttles were steady
and full. I estimated the aircraft speed at between 350 and 400
knots. The flight path appeared to be deliberate, smooth, and
controlled. As the aircraft approached the Pentagon, I saw a minor
flash (later found out that the aircraft had sheared off a portion of
a highway light pole down on Hwy 110). As the aircraft flew ever
lower I started to lose sight of the actual airframe as a row of
trees to the Northeast of the FOB blocked my view. I could now only
see the tail of the aircraft."

Morin indicates that the plane was not directly over his head as he
was able to see its markings, not visible from beneath.

"I estimate that the aircraft was no more than 100 feet above me
(30 to 50 feet above the FOB) in a slight nose down attitude. The
plane had a silver body with red and blue stripes down the fuselage.
I believed at the time that it belonged to American Airlines, but I
couldnt be sure."

Morin describes the plane traveling parallel to the Navy Annex and
flying straight, directly toward the Pentagon. Given that he was on
the ground near the Annex, only if the plane is on the south path,
flying straight to the Pentagon, will it remain in his line-of-sight.
CIT ignores his description of the path of the plane and claim him as
a north path witness, though from his statement he must be a south
path witness. CIT states that there is no south path witness; clearly
we have found one already.

5. Albert Hemphill, interviewed by Craig Ranke of
CIT:
30
"Looking out the window thinking to myself, my God, whats this
world coming to ... then I hear a roar and look out the window at the
plane ... over my right shoulder ... over the gas station ... clipped
a light pole ... diving ... right over the bridge ... smacked right
into the building."

Ranke then asked if it passed to the south of the VDOT antenna tower.

"That would be a bit far." [Note that the VDOT antenna would not
have been in Hemphill's view. He did, however, state that he was
aware of its location.] "I saw one plane and I saw it hit... it
didnt pull up, it didn't turn right, it didn't turn left, it
went right into the Pentagon."

It is worth noting
that Ranke is willing to lead a witness to get confirmation of his
hypothesis, as his interview with Hemphill demonstrates. Hemphill
initially paints a picture that is contrary to the NOC hypothesis.
Ranke responds by telling him about several other witnesses by name,
and saying "it's rather compelling watching all these accounts
match over and over and over and all describing the plane flying in
the exact same place," which was "between the gas station and
Arlington cemetery." Hemphill concedes that they could be right
because anyone "out and about" would have a great vantage point.
This is not to be confused with his own direct testimony, however,
which is that the plane flew over his right shoulder, not far from
the VDOT tower, went right over the "bridge" (clearly indicating
the overpass of VA27 over Columbia Pike), clipped a light pole, flew
close enough to the ground that he would speculate about "ground
effect," and hit the building at the level of the second row of
windows. This path is entirely south of the Citgo gas station and in
line with the trail of damage outside and inside the building, so
Hemphill is clearly another south path witness, yet CIT claims him as
a NOC witness. In light of the Asch Conformity Experiments, telling a
witness what other witnesses have said invalidates the independence
and validity the data.
31

It should also be
noted that this interview was carried out years after the event. Had
Hemphill been standing at his office window when he was interviewed
he would not have made the mistake of thinking the path might have
been over or north of the Citgo service station. His line of sight
from his office window to the impact point passes directly over the
service station (see Fig. 3), so he was particularly well placed to
judge that the path he clearly remembered, and asserted in all his
statements, was to the south. He insisted that the path was straight,
so could not have deviated round the Citgo service station. Again we
have an interview that was not carried out on location, with no
mention being made that this is another exception to their claim of
reliability due to location. Hemphill was irritated by the pressure
of the questioning and remarked "I saw what I saw. That is where it
stands."

It is important to
note that several of the witnesses Ranke was quoting "over and
over" were near the Arlington cemetery. It is not reasonable to
assert they could accurately judge from that distance that the plane
was a little north or a little south of the Citgo service station. In
contrast it would be easy for them to judge whether the plane was
steeply banked, but all these witnesses stated the plane flew "flat"
over the Annex and then banked only slightly, or made no mention of
an unusual steep bank angle.
32
Hemphill's words "it didn't turn right, it didn't turn left"
correspond with Bogers phrase "it didn't veer" and with
Morins assertion that the plane was "heading directly towards
the Pentagon". All these observations contradict the NOC path, as
will become apparent below where we discuss the angle of bank
required.

The evidence to this
point leads us to infer that CIT has misled the public in regard to
the witness testimonies, having failed to present the evidence of
Lagasse, Turcios, Brooks, Paik, Morin, Hemphill and Boger fairly. It
is our purpose to add another dimension to this discussion.

Analysis

Let us examine the
dynamic feasibility of a NOC flight path.

Radar could not
provide useful information close to the Pentagon as, by then, the
plane would be too low, but radar tracks from four different
facilities corroborate each other, leading directly toward the
Pentagon. The track from the nearest radar facility, at Ronald Reagan
National Airport, reaches to a point only about 6 seconds prior to
impact. This is close enough to the Pentagon to indicate that
all the witnesses who mentioned the distance from themselves to the
plane underestimated the distance, as can be seen in the following
image (Fig. 1).
33
Recall, for instance, that Deb Anlauf at the Sheraton, about 500 feet
from the radar track, describes the plane as right outside her
window saying, "You felt like you could touch it; it was that
close." Perhaps we underestimate distances in situations like
this because we are not used to seeing large planes flying so low and
interpret the large size as indicating closeness. From a statistical
point of view it is unfortunate that there are many witnesses who
were north of the path and few who were south of the path, close
enough to form a clear impression of the position of the track, hence
it is not surprising that there should be some northerly bias in the
reporting. The FDR data extends the radar data for about 6 more
seconds (Fig. 1) and shows no deviation right to the Pentagon.

Figure 1:
Four radar tracks approach the Navy Annex. The yellow line is the
last 20 seconds of the FDR data, aligned with the trail of damage. It
shows no deviation over this distance.

The testimony of the witnesses cited above is in reasonable
conformity with the path defined by the radar data, the FDR data and
the damage trail. Some witnesses said the plane was coming along
highway 395; some said it was coming along Columbia Pike, which runs
close to the south side of the Navy Annex, nearly parallel with the
closest section of highway 395. To be consistent with these witnesses
the plane must have passed south of the Sheraton Hotel, south of the
A-1 Car Repair shop of Ed Paik, and near Terry Morin. Morin may have
been between the wings of the Navy Annex as the plane flew over, but
said that he "ran to the outside" from between the wings to a
"position where I could see it."
34
"As he starts to descend ... he basically starts to disappear ...
the engines disappear, the bottom of the fuselage, the wings..." He
followed the plane as it dipped down over a row of trees on its
approach to the Pentagon until all he could see was the tail. He does
not mention bank angle.

Taken at his word, Morin witnesses a direct approach to the Pentagon
along the south path. We will, however, loosen that assumption to
enable our discussion to proceed further and in our initial analysis
will simply assume the plane does not veer north until it has passed
Morin. Already this conflicts with Morins testimony, in that it
cuts short the distance that it would be visible to him, as will
become evident below.

To favor the NOC hypothesis as much as possible, we assume that the
plane passed barely north of Citgo, in fact flying directly over the
northernmost corner of the station. Finally we assume that, in order
for the alleged "magic trick" with the smoke to work, the plane
flew directly over the impact point on the west face of the Pentagon.
For the sake of argument, we set aside the numerous observations of
impact, the observations of the plane hitting light poles, a fence
and a generator, and observations that it flew straight and descended
very close to the ground.

For the plane to follow a path that conforms with the remaining
constraints, it must deviate from its initial path. It must first
turn left and then turn right. Turns for aircraft involve banking and
heightened g-force, which is the apparent gravity induced by
centripetal acceleration. We make the assumption that the radius of
curvature, and hence the g-force, is equal for the left and
right banks. This is the assumption most favorable to the NOC
hypothesis. Furthermore, for a large plane to transition from a hard
left bank to a hard right bank requires a roll maneuver, which takes
some time. For simplicity we assume that the plane flies straight
during the brief transition from left bank to right bank. Fighters
are small and have their mass close to the longitudinal axis of the
plane, so they can roll quickly. Large planes, with their outboard
engines and heavy fuel tanks in the wings, have a large moment of
inertia and would require several seconds to make the transition.
However, for the sake of argument we will consider the implausibly
short left-to-right roll times of one second, and one half second.
Shortening the assumed roll time allows more space for the bank
maneuvers, thus favoring the NOC hypothesis.

Aircraft speed

Speed is important as it is one of the two factors which determine
angle of bank. Some of CIT's witnesses estimate speeds of 350 to 400
mi/hr. These low estimates are uncalibrated guesses. There is good
reason to believe that the testimony by the same and other witnesses
that the plane was accelerating is more reliable, since it was based
on the sound of the motors revving up. The distinctive sound of the
engines would be more reliably assessed than the speed of the plane
itself as our ears are sensitive to pitch. It is understandable that
visual estimates of speed would be low, given that all the observers
perceived the plane to be closer than it really was. If an object
moving across the field of view is farther than the viewer estimates,
the reduced angular motion across the field of view, due to distance,
will be misinterpreted as being due to lower speed. Several witnesses
use words like "spooling up," "full throttle," and "powered
descent" to describe what they heard.
35
We recall that Morin said he heard a "... steady high-pitched
whine" indicating to him that "the throttles were steady and
full." The plane was also diving, so it had assistance from gravity
in gaining speed. The FDR data indicates an average ground speed of
552 statute miles per hour (mi/hr) for the last 4 seconds and the
final speed measured prior to impact was 556 mi/hr. The official
estimate is 530 mi/hr, which is presumably based on the final speed
shown in the original improperly decoded FDR file, 465 knots (535
mi/hr). The FDR file also shows that the engines were suddenly set to
full power for the last half minute, during which time the plane
accelerated rapidly and uniformly. Measurements of the radar
positions, recorded every 4.7 seconds, shown in Fig. 1, provide
independent confirmation of the speed and acceleration, as shown in
Fig. 2. Distances were calculated using the Haversine method for
great circle arc length, spherical earth approximation, from latitude
and longitude.

Figure 2:
Radar data from Ronald Reagan National Airport (the nearest
source) confirm the acceleration shown in the FDR file, in conformity
with witness reports of hearing the engines "spooling up".

A trend line through this period gives a last 4.7 second interval
averaging 520.2 mi/hr, accelerating at 6.39 mi/hr/s. Extrapolation of
these figures to the next interval would give an average speed of
550.3 mi/hr, and after a further 2.35 seconds to the end of the
interval, which would be very close to the moment of impact, the
speed would be 565.3 mi/hr.

The last measured speed in the FDR file was 556 mi/hr. This is
recorded in word 94. The impact is recorded in word 225, thus 131
words later. Each word is 1/256th of a second hence 0.51
seconds elapsed prior to impact. If the calculated acceleration was
maintained during this period the final speed would be 559 mi/hr. The
radar data thus lead to a final estimated speed which corresponds
well with the FDR file.

As this plane, known to be aerodynamically efficient, was clean and
diving, it could not possibly slow down significantly in those last
few seconds as it passed the Navy Annex, even if, contrary to witness
reports, it was throttled right back. Given the weight of evidence
from the FDR file and radar, and the witness reports of the engine
power rising, we reject the low speed estimates of 350 to 400 mph as
flawed visual estimates without evidence. We will base our
calculations on the official speed, 530 mi/hr, as a low estimate, and
the FDR speed, averaged for the last four seconds, 552 mi/hr, as the
more realistic estimate.

Computation of the g-forces involves a calculation based on
the speed and the radius of curvature of the path. To determine the
gentlest possible turns we used Geogebra, which is a free, open
source, geometry software tool. We devised a geometrical construction
such that given an approach line, a turn-off point on the line, a way
point (labeled North Citgo in the diagrams), a target point, and
duration for the roll maneuver, we could produce left and right arcs
with equal radii and a straight segment between them, mutually
tangent to the two arcs, representing the roll maneuver. Fig. 3
illustrates a typical result.

Figure 3:
Path along the FDR route with turnoff level with Morin, 1 second roll time.
The FDR track is shown in yellow, the left and right banks in red and the
roll time in orange.

For a turn-off point level with Morin, with a 1 second roll time the
results are:

Speed (mi/hr)

Bank Angle

g-force

552

85.2

12.1

530

84.8

11.0

The design limit for
a Boeing 757 is 2.5g. Even if the plane somehow held together, it
would be impossible to control during such an extreme maneuver.

If we reduce the
roll time to (a clearly fictitious) one half second the values
improve somewhat, but not enough to bring them within the range of
plausibility:

Speed (mi/hr)

Bank Angle

g-force

552

84.7

10.7

530

84.2

9.9

Note that this scenario already conflicts with the testimony of Morin who stated
that he watched the plane fly a considerable distance and descend
behind a row of trees, with only the tall tail fin eventually being
visible. It can be seen from the diagram (Fig. 3) that the plane
would pass too quickly out of his line of sight. Note also that in
this case the plane would disappear left wing first, his view
obstructed by the vertical wall of the Annex, whereas we recall that
he describes the plane disappearing from the bottom up, so his view
must have been obstructed horizontally by the trees. We also see that
witnesses would have seen the plane change from a steep left bank to
a steep right bank between the Annex and the Citgo service station,
but no such maneuver was reported.

If we now discount
Morins description of the path of the plane entirely, and allow
that he did not see it at all after it passed him, we can construct a
scenario more favorable to the NOC hypothesis by moving the turn-off
point earlier (Fig. 4). The last radar position provides the earliest
point that the turn can reasonably be commenced. Morin's observation
that the plane flew nearly overhead is found to be preserved. Note
that the curves are gentler.

This scenario, which
totally disregards the testimony of Morin regarding the path of the
plane (and there appears to be no justification for doing so) shows a
substantially reduced g-force. It is still so high, however,
that only someone with the skills of a trained fighter pilot would
have a chance of performing it. The bank angle is still extremely
steep.

The extraordinary
bank angle

Anlauf and Paik
would have seen the plane in a steep left bank and Morin would have
seen it in a steep right bank. Hemphill would have seen the plane
crossing from right to left of his line of sight to the impact point,
at a steep right bank, as he looked out of his office window (Figs. 3
and 4 show his vantage point). These people reported no such thing.
Hemphill repeatedly asserted that the plane was on his right and
flying straight, and therefore with no significant bank. In the FDR
file the maximum bank briefly recorded during this period was just
6°.

For these scenarios
to work, the plane, after the roll, must maintain the steep right
bank all the way to the Pentagon if it is to reach its target, which
means the fuselage would have had to clear the roof of the Pentagon
by nearly a wing-length, further straining the credibility of the
"magic show" hypothesis.

The bank angle in
all of these runs is so far out of the range of normal that, if it
had happened, it would have astonished all observers. It would have
been widely reported, yet nobody reported more than a slight bank.
Albert Hemphill described the plane so close to the ground that he
speculated about ground effect, which is clearly inconsistent with
any of the calculated bank angles. Several of the witnesses indicated
that the plane was flying "flat" in the vicinity of the Navy
Annex, hence flying straight.36
This is totally at odds with the necessary curve and bank angle.

CIT has provided
assistance here, handing some witnesses a model plane so that they
could illustrate the bank. The bank they show is slight. In
particular we note that not one of the 13 witnesses, who claimed they
saw the plane well enough to believe that it was NOC, mentioned that
it was extremely steeply banked. The bank angle would have been
glaringly obvious and, because of its strangeness, unforgettable.

Notes on the Calculations

The images used for these constructions are from Google Earth, with the
history rolled back to September 12, 2001, (or September 13 for those
of us west of the International Date Line). Note that, due to the
camera location for this particular photograph, the roofs of the
buildings are displaced a little south east relative to the
footprints at ground level. The undulation of the landscape can
induce similar small displacements. Positions relative to the
footprints of buildings were used to avoid the former effect, and
care was taken to centralize the point of interest in the screen,
while placing markers, to minimize the latter. Since Geogebra is
free, open source software, the reader can easily confirm this work
and try other variations. We would like to thank the authors of
Geogebra for the wonderful tool they have made freely available to
the public.

The construction we
used produces two arcs of equal radius separated by a stated interval
along a mutual tangent (the roll interval), with one arc tangent to
the path of approach and the other passing through a way point and
the target. Deriving the construction is left as an interesting
exercise for the reader.

Once having
determined the radius of the path, it is possible to calculate the
centripetal acceleration for any speed using:

a = v2/r

where a is
acceleration, v is velocity and r is the curve radius.

Centripetal acceleration produces the sensation of an outward
"centrifugal" force which feels like gravity. This can be
expressed as a horizontal g-force, gh,
by evaluating the ratio:

gh = a/g

where the
denominator, g, (for Washington D.C.) is 9.801 m/s/s in SI
units or 32.16 ft/s/s in imperial units. The bank angle is found from
arctan(gh).

For a plane
maintaining altitude in a turn, the sideways "pseudo gravity" is
combined with the downward actual force of gravity, to give the total
or resultant force, gt, using the
Pythagorean Theorem:

gt =
√

gh2 + 12

CIT videos
illustrate their concept of the flyover with a plane slipping
unnoticed over the roof of the Pentagon in a horizontal orientation
hidden by the smoke cloud. Referring again to the work of Jim
Hoffman, who shows how easy it would be to see the plane flying over
the Pentagon, even in a horizontal orientation, consider how
remarkable his images would appear if he showed the fuselage a
wing-length above the roofline at a bank angle of 77°, and the other
wing protruding an equal distance higher, as it started to fly over
the Pentagon.

Figure 5:
Imagine how riveting Jim Hoffman's scene would be if
the plane were banked at 77°.

We have shown that
at the very high speed the plane was traveling, and with the very
short distance available for the turn, even a slight deviation from a
straight path would require a steep bank angle. We can safely
conclude that the plane must have been flying virtually straight,
since many witnesses affirm and none (including those who reported a
NOC path) deny that the plane was close to level. To claim that the
plane could follow the NOC path without banking very steeply is to
defy the laws of physics.

It should also be
noted that the plane is being asked to do two difficult things
simultaneously. On the one hand it must bank steeply to force the
plane round the required curve. On the other hand it must pull out of
the rapid descent which witnesses describe. The FDR data show that
the pull-up was largely confined to the last 2 seconds of flight and
that an upward force was generated of about 2g. This would be easy
for a plane which is close to level but at a bank angle of 77° the
problem posed is far more difficult. The pilot, already pulling back
hard on the control column to achieve the turn, would have to turn
the wheel left to reduce the bank and create lift. This will use up
some of the distance available for the turn. The pilot would have had
to anticipate this need and start his turn even more steeply, and
with more g-force than calculated above, in order to still arrive
above the point where the smoke was to be generated.

Even if the pilot
managed to work all this out, and apply it at the precise moment
required, he could not avoid passing over the Citgo service station,
and some distance before and beyond, steeply banked, but this was not
observed. It is evident that it did not occur.

Given that there is
no evidence the plane was steeply banked, and ample evidence that any
bank was slight, simple physics and geometry show that the curved NOC
path must be false. Furthermore there is no rational justification
for the perpetrators to make the extremely difficult maneuver, which
would not only endanger the plane but would also put the entire
project at risk of failure.

No one has made a
case for flyover on a direct approach, and there is no evidence for
such an event. Voluminous eyewitness testimony, independent radar
tracks from four separate agencies, the FDR data and the damage
trail, place a large aircraft, consistent with a 757, at the scene
approaching the Pentagon at a low level, at high speed and still
accelerating. Impact with the Pentagon therefore cannot be avoided.
It follows that the CIT claim that it would be impossible for the
plane to do the observed damage, and that explosives would be
required, is also false.

The claim by CIT that the plane flew NOC, strengthened by incorrect
calculations published by PFT, has caused many researchers to pay
attention to arguments that suggest the plane did not hit the
Pentagon. Those who have been convinced by a few photographs that
appear to show a hole too small, or insufficient debris outside the
Pentagon, are advised to reconsider the work of Hoffman,
37
Legge,
6
and others who have done a
careful analysis of the plausibility of a 757 collision. It will be
found that all of these arguments are flawed or unsubstantiated,
leaving impact with the Pentagon as the only reasonable conclusion.

Summary and
Conclusion

The calculations we
have displayed here show extreme values for the g-force
required to deviate from the initial path to pass north of the Citgo
service station, 4.3g being the lowest conceivable value, requiring
that Morins testimony be totally set aside for no apparent reason,
and the impossible 12.1g if some of Morins testimony is accepted.
The bank angles are even more telling, since they would be clearly
observable, 77° being the lowest possible. These values are
confirmable by the reader using free software tools.

The force calculated
is well beyond the design limit for this aircraft, 2.5 g, and also
above the likely strength safety margin. Control of the aircraft,
even at the lowest computed g-force, would be impossible for
other than a highly trained aerobatic pilot and the physical survival
of the aircraft would be at least in doubt.

The bank angle would
be so steep as to astonish observers and be well remembered and
frequently reported, but steep bank angles were not reported at all.
Nothing more than a slight bank was described, even by those
observers who claimed to see the path of the plane clearly enough to
feel sure it was north of the Citgo service station.

It is physically
impossible for a passenger plane to pull sharply out of a descent at
a steep bank angle. The plane was descending steeply but managed to
quickly level off, hence could not have been steeply banked.

It is physically
impossible for any plane to pass NOC at the reported speed without
banking steeply, hence the few witnesses who claimed to have observed
the north path were necessarily mistaken about the path of the plane.
Several such witnesses reported that the plane was flying level in
the vicinity of the Navy Annex, in complete contradiction of the
curved NOC path.
36
The NOC witnesses are outnumbered by
witnesses to impact by about 10 to 1, or about twice that if we
disqualify the NOC witnesses who contradicted themselves by reporting
that they saw the impact. There is a complete absence of witnesses to
the plane flying over the Pentagon, though hundreds of people were in
a position to see it and the sight would have been striking,
commencing, or approaching, with a remarkably steep bank.

If, as we have shown,
the plane did not fly north of the Citgo service station there
is no reason to suspect that it did not hit the Pentagon. If it was
flying close to the ground in the vicinity of the light poles, as
described by many witnesses, it could not miss. The FDR file, the
damage to the light poles, the fence and the generator and the shape
of the damage on the face of the Pentagon all indicate impact. All
arguments used to suggest that the plane could not have hit the
Pentagon have been shown to be unfounded.
376
CIT is shown to be presenting a hypothesis which is physically
impossible. According to the scientific method this hypothesis must
be abandoned.

It is to be hoped
that those who have been puzzled by the apparently contradictory
assertions surrounding the Pentagon attack, will now see that it is
appropriate to withdraw support for the divisive notion that no plane
hit the Pentagon. There are many disturbing issues which deserve our
close attention related to the Pentagon attack, as have been clearly
set out by Kevin Ryan
38
and others, but the question of whether a plane hit the Pentagon
should not be on that list.

5
Pilots for 9/11 Truth states on their website: "Physically and
aerodynamically, Arlington's unique topography and obstacles along
American 77 "final leg" to the pentagon make this approach
completely impossible as we will demonstrate.",
http://pilotsfor911truth.org/descent_rate031308.html

13
Collection of Pentagon attack information. The link to the Excel
file, which lists witnesses by their type of report, is convenient
and still functioning. 136 saw a plane, 104 saw it hit.
http://sites.google.com/site/wtc7lies/911pentagonflight77evidencesummary

33
Thanks to John Farmer, who kindly provided radar
positions which he calculated, using proper adjustments for azimuth
angle, from raw data he had obtained using FOIA.

34
Morin, T., by Craig Ranke,
http://www.youtube.com/watch?v=cJKITI1gn4g
In this video at 7:47 we see that the
top of the Pentagon is visible, thus Isobel James would have been
able to confirm impact as, if the plane became hidden behind trees,
she would see that it did not emerge. At 7.55 we hear Morin describe
how the plane disappears from the bottom up.

36Witnesses near the cemetery who indicated the plane was not consistently banked:
At 34:22 in
http://www.youtube.com/watch?v=j5FhQc-LJ-o
W. Middleton shows a flat hand gesture then wobbles his arms and says
"while descending he was straightening..."
He shows no indication of sustained bank. At 37:30 D. Stafford says
"It was flat, just on top of the roof [of the Navy Annex]"
and holds the model plane level. He shows the plane descending then banking
to about 30 degrees. D. Prather also holds the model plane level as he says
"across the Navy Annex," He too shows the plane descending before it banks.
This bank is too little, too late.